In previous works (JHEP03(2012)100, JHEP09(2012)015), we have highlighted that the Higgs and Z-mediated penguin diagrams contributing to lepton flavour violating (LFV) observables like tau->3mu are strongly enhanced in the supersymmetric inverse seesaw model. It has recently been pointed out that an error in the literature for the Z-penguins form factors would lead to a non-physical non-decoupling behaviour (1312.5318). This work is devoted to the study of LFV lepton decays and mu-e conversion in the supersymmetric inverse seesaw, taking all contributions into account with the corrected form factors. We explicitly distinguish various regimes depending on the dominant contribution and give predictions for various observables, some of them already within reach of the current experiments.